How much medical cover do I need for the USA?
More than you think, and more than a basic European policy carries. As a rule, look for a medical limit measured in millions rather than thousands, because US hospital bills and air ambulance repatriation sit at the extreme end of what travel insurance ever has to pay. This is not the trip to economise on the medical limit.
If you travel to the USA as well as elsewhere in the year, an annual worldwide policy including the USA covers every trip under one arrangement.